|
%I #21 Jun 13 2015 00:49:20
%S 1,1,2,5,7,12,103,115,218,551,769,1320,11329,12649,23978,60605,84583,
%T 145188,1246087,1391275,2637362,6665999,9303361,15969360,137058241,
%U 153027601,290085842,733199285,1023285127
%N Denominators of continued fraction convergents to sqrt(21).
%H Vincenzo Librandi, <a href="/A041033/b041033.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,110,0,0,0,0,0,-1).
%F a(n) = 110*a(n-6)-a(n-12). G.f.: -(x^4-x^3+2*x^2+x+1)*(x^6-6*x^3-1)/((x^4-5*x^2+1)*(x^8+5*x^6+24*x^4+5*x^2+1)). [_Colin Barker_, Jul 16 2012]
%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[21],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 17 2011 *)
%t Denominator[Convergents[Sqrt[21],30]] (* _Harvey P. Dale_, Apr 22 2013 *)
%t CoefficientList[Series[- (x^4 - x^3 + 2 x^2 + x + 1) (x^6 - 6 x^3 - 1)/((x^4 - 5 x^2 + 1) (x^8 + 5 x^6 + 24 x^4 + 5 x^2 + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 22 2013 *)
%Y Cf. A010477, A041032.
%K nonn,cofr,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
|
